When it comes to past time travel and paradoxes...
Is much like an equation in which 2 or more variables are unknown and not enough information is possible to solve for both. Also, assume paradox's had the outcome of Doctor who, in that if you went back intime and caused something to change, thus changing you ever going into the past. The timeline resets itself to right before you travel to the past not knowing anybetter.
Now, assume like said engineering math equation to solve for both variables you must iterate, using a educated guess for X to find Y, which you plug back into Y to find X, which you plug back into X to find Y, thus iterating the values of X and Y until they converge onto true values of the equation (normally used in pressure and temperature curves in vapor and bubbles).
Now let us assume time travel is the same way. Everytime you go into the past you cause a paradox, it resets back to right before you go back into the past. Thus Eventually you will do something the way it was intended to cause the future you live in to be that future that you didn't know was caused by you before, or iterate another time until a paradox no longer exists. (basically going in circles until the one time it doesn't cause a paradox)
Thus if the universe was to act in such a manner, past time travel could be done without paradoxes happening and without the need of a alternate univers loophole (if we could ever actually time travel).
The alternate universe theory is used to break any possible paradox that could occur. Because once you go into the past, you are now a seperate being of your past self, and thus it willnot effect your future self since you are theoretically in another universe in which all is the same except the past you didn't learn to time travel.